Handbook of Atomization and Sprays

This chapter deals with capillary instability of straight free liquid jets moving in air. It begins with linear stability theory for small perturbations of Newtonian liquid jets and discusses the unstable modes, characteristic growth rates, temporal and spatial instabilities and their underlying physical mechanisms. The linear theory also provides an estimate of the main droplet size emerging from capillary breakup. Formation of satellite modes is treated in the framework of either asymptotic methods or direct numerical simulations. Then, such additional effects like thermocapillarity, or swirl are taken into account. In addition, quasi-one-dimensional approach for description of capillary breakup is introduced and illustrated in detail for Newtonian and rheologically complex liquid jets (pseudoplastic, dilatant, and viscoelastic polymeric liquids).

This chapter deals with liquid jets bending due to the aerodynamic interaction with surrounding air or buckling due to the impingement on a solid wall. The experimental evidence is considered and linear and nonlinear theories describing perturbation growth developed in the framework of the quasi-one-dimensional equations of the dynamics of liquid jets moving in air are discussed. Jets of viscous Newtonian or rheologically complex liquids (in particular, viscoelastic polymeric liquids) are considered. In addition, bending instability of the electrified liquid jets (in particular, polymeric liquid jets in electrospinning) is considered. In the latter case, both the experimental and theoretical aspects are tackled.

This chapter relates to the liquid sheets and their instability. Liquid sheet instability is due to the interaction between the liquid and its surrounding fluid. When the amplitude of a perturbation grows and reaches a critical value, sheet is disintegrated forming liquid ligaments. Here, the linear and nonlinear instability of an inviscid and viscous liquid sheet is discussed, showing the effect of the aerodynamic forces on the growth rate of the initially small perturbations. Other effects, such as the effect of initial velocity profile on the instability are also discussed.

In this chapter the basic physics and methods of calculation of the effective drag forces acting on drops in isolated-drop and multidrop configurations relevant to sprays are provided. The effect of various physical phenomena such as drop deformation, nonuniformity of the incoming flow, drop–drop interactions, drop–gas interactions, and evaporation on the drag coefficient on the drop, with special focus on the underlying physics, is highlighted.

A liquid droplet may go through shape oscillation if it is forced out of its equilibrium spherical shape, while gas bubbles undergo both shape and volume oscillations because they are compressible. This can happen when droplets and bubbles are exposed to an external flow or an external force. Liquid droplet oscillation is observed during the atomization process when a liquid ligament is first separated from a larger mass or when two droplets are collided. Droplet oscillations may change the rate of heat and mass transport. Bubble oscillations are important in cavitation problems, effervescent atomizers and flash atomization where large number of bubbles oscillate and interact with each other. This chapter provides the basic theory for the oscillation of liquid droplet and gas bubbles.

Following formation, droplets may enter a region where aerodynamic forces are large enough to cause significant deformation and breakup. When a droplet breaks apart into a multitude of small fragments due to disruptive aerodynamic forces, the process is termed secondary atomization. This has been a rich area of study for many years and a number of in-depth reviews are available [1–4]. Here, the most important findings are discussed. The chapter is divided into two sections: Newtonian and non-Newtonian liquids.

Droplets may be accelerated from rest gently or by a near step change in relative velocity. Experimentation has shown that the breakup is different in each case. The first case is found in nature and plays an important role in rain storms. However, the latter is more likely to occur in sprays. For this reason, this chapter considers only breakup due to step changes in relative velocity.

We put together the state of knowledge on binary collisional interactions of droplets in a gaseous environment. Phenomena observed experimentally after drop collisions, such as coalescence, bouncing, reflexive separation and stretching separation, are discussed. Collisions of drops of the same liquid and of different – miscible or immiscible – liquids, as well as collisions of drops of equal and different size are addressed. Collisions of drops of immiscible liquids may lead to an unstable interaction which is not observed with drops of equal or miscible liquids. Regimes characterized by the various phenomena are depicted in nomograms of the Weber number and the non-dimensional impact parameter. The state-of-the-art in the simulation of binary droplet collisions is reviewed. Overall three different methods are represented in the literature on these simulations. We discuss models derived from numerical simulations and from experiments, which are presently in use for simulations of spray flows to account for the influence of collisional interactions of the spray droplets on the drop size spectrum of the spray.

This chapter considers droplet-wall interaction and droplet impact and splashing on a solid surface. The discussion on droplet-wall interaction considers thermo-fluid-dynamic processes associated with droplet impact onto solid surfaces. The emphasis is put on the disintegration mechanisms as an introduction to the intricate interaction phenomena occurring at spray impingement. The analysis starts with the simplest situation of single droplet impacts onto non-heated and dry surfaces; further complexities are then introduced which consider the interaction with a liquid film and the combined effects of heat transfer. The discussion on droplet impact and splashing on a solid surface includes splashing and fragmentation of molten metal and other liquid droplets landing on a solid surface. Issues such as different types of splashing, corona splashes, freezing induced splashing are considered from an experimental point of view.

In an effort to characterize fuel sprays using Computational Fluid Dynamics (CFD) codes, a number of spray breakup models have been developed. The primary atomization of liquid jets and sheets is modeled considering growing wave instabilities on the liquid/gaseous interface or a combination of turbulence perturbations and instability theories. The most popular approaches for the secondary atomization are the Taylor Analogy Breakup (TAB) model, the Enhanced-TAB (E-TAB) model, and the WAVE model. Variations and improvements of these models have also been proposed by other researchers. In this chapter, an overview of the most representative models used nowadays is provided.

This chapter discusses flashing in spray nozzles. Different physical aspects involved in flashing such as phase change, bubble nucleation, bubble growth, internal two-phase flow and flash atomization are discussed. The effect of flashing on droplet size and velocity are also discussed.

A supercritical fluid is defined as one that is above its thermodynamic critical point, as identified by the critical pressure (

p

c

) and critical temperature (

T

c

). Supercritical fluid behavior can be peculiar because of the variation of thermophysical properties such as density and specific heat near and at the critical point. Supercritical fluids have some properties similar to liquids (e.g., density), and some properties that are comparable to those of gases (e.g., viscosity). Thus, they cannot be considered either a liquid or a gas.

Evaporation of multi-component liquid droplets is reviewed, and modeling approaches of various degrees of sophistication are discussed. First, the evaporation of a single droplet is considered from a general point of view by means of the conservation equations for mass, species and energy of the liquid and gas phases. Subsequently, additional assumptions and simplifications are discussed which lead to simpler evaporation models suitable for use in CFD spray calculations. In particular, the heat and mass transfer for forced and non-forced convection is expressed in terms of the Nusselt and Sherwood numbers. Finally, an evaporation model for sprays that is widely used in today’s CFD codes is presented.

The classification regimes for premixed and non-premixed combustion processes are discussed in terms of the Damköhler and Karlovitz numbers. Dec’s diesel spray combustion concept is introduced, followed by a short review of chemical kinetics. The ignition process together with appropriate models is then discussed. Subsequently, various combustion models are presented, including mixing-controlled, flamelet and PDF combustion models. The chapter ends with a discussion of pollutant modeling for nitric oxides (NO) and particulates.

Starting from a consideration of microscopic flame propagation modes between neighboring droplets and macroscopic flame propagation modes in spray elements, the excitation mechanism of group combustion (diffusion flame enclosing droplets) is described for an example of atomizing liquid fuel jet issuing into an otherwise stagnant oxidizing atmosphere.

At low pressures, the evaporation rate of a droplet is not adequately described by the equations of continuum mechanics, that is, by mass diffusion and conduction heat transfer. When the mean free path of the evaporated molecules is large compared with the droplet radius, the kinetic theory of gases can be applied to determine the evaporation rate. In this limit, the free-molecule regime, it is assumed that the molecules have a Maxwell-Boltzmann distribution of molecular velocities. In the intermediate regime, the Knudsen regime, molecular collisions distort the Maxwell-Boltzmann distribution and reduce the rate of transport of the molecules leaving and arriving at the droplet surface. This chapter reviews the theory and measurements of droplet evaporation in the free-molecule and Knudsen regimes.

Freezing and solidification processes are discussed and modeled for liquid droplets which undergo first-order phase transitions. First, a four-stage model is presented which accounts for supercooling, nucleation, recalescence, and crystallization. Subsequently, a more detailed discussion of a three-stage solidification model for droplets that do not exhibit supercooling is given. Aspects of the three-stage model validation are presented for a single cocoa butter drop and for a cocoa butter spray.

This chapter provides an overview of the techniques available to deal with flows having liquid-gas interfaces. These techniques are categorized based on the type of flow modeling (Eulerian, Lagrangian, or mixed), type of interface modeling (capturing or tracking), flow–interface coupling (integrated or segregated), and the type of spatial discretization (meshless, finite difference, finite volume, finite element [FE], or others).

This chapter reviews atomization modeling works that utilize boundary element methods (BEMs) to compute the transient surface evolution in capillary flows. The BEM, or boundary integral method, represents a class of schemes that incorporate a mesh that is only located on the boundaries of the domain and hence are attractive for free surface problems. Because both primary and secondary atomization phenomena are considered in many free surface problems, BEM is suitable to describe their physical processes and fundamental instabilities. Basic formulations of the BEM are outlined and their application to both low- and high-speed plain jets is presented. Other applications include the aerodynamic breakup of a drop, the pinch-off of an electrified jet, and the breakup of a drop colliding into a wall.

In this chapter, the mathematical description of spray processes is presented. After a brief summary of the basic mathematical concepts used, a discussion of the conservation equations is given, followed by a brief introduction to turbulence. Subsequently, a discussion of turbulence modeling is presented including Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) modeling. Once this basic background is established, the discussion of the averaged or filtered conservation equations in conjunction with the liquid phase equations is given. The chapter ends with a discussion of the discretization of the equation system and the main algorithms used for the numerical solutions.

Among the noncontinuum-based computational techniques, the lattice Boltzman method (LBM) has received considerable attention recently. In this chapter, we will briefly present the main elements of the LBM, which has evolved as a minimal kinetic method for fluid dynamics, focusing in particular, on multiphase flow modeling. We will then discuss some of its recent developments based on the multiple-relaxation-time formulation and consistent discretization strategies for enhanced numerical stability, high viscosity contrasts, and density ratios for simulation of interfacial instabilities and multiphase flow problems. As examples, numerical investigations of drop collisions, jet break-up, and drop impact on walls will be presented. We will also outline some future directions for further development of the LBM for applications related to interfacial instabilities and sprays.

Spray-wall impact is an important process in numerous applications such as internal combustion (IC) engines, spray cooling, painting, metallurgy, and many others. This chapter reviews the main challenges in this dynamic thermofluid event and attempts to systematize the knowledge developed in the hydrodynamics of multiple drop impacts and liquid deposition, the statistical analysis of secondary atomization after impact, and the thermodynamics underlying heat transfer processes in spray impaction onto heated surfaces.

In many disparate engineering systems, ranging from cooling systems for microelectronics to jet engines, multiple sprays are utilized and the way they interact with one another is the subject matter of this chapter. A general overview of published research on interacting sprays is presented. Both experimental and theoretical or numerical investigations of combusting or noncombusting systems are covered. The nature of the interactions may be either direct (with actual contact between the sprays) or indirect (with no contact between the sprays). It is found that, despite the underlying common physics which reflects the mutual interaction between the sprays and their surroundings and between themselves, with few exceptions the material in the literature tends to relate to the impact of spray interactions

in specific systems

rather than on the fundamentals of the interaction. The question that is addressed is: is the use of multiple sprays more effective than the use of a single spray, or is it possibly detrimental? And, if the latter is true, can the situation be ameliorated by manipulation of the physics through geometric and other factors that relate to the sprays? Surveying the sparse literature on this subject gives some inkling of the important features that are relevant at a basic level. But much remains to be done, both experimentally and theoretically, in order to fully elucidate the complexities of spray interactions.

Drop size distributions are at least as important as mean drop sizes. Some spray applications require narrow size distributions (paint and respirable sprays), while some need wide ones (gas turbine engines). Other spray processes require very few small drops (agricultural or consumer product sprays) or very few large ones (waste incineration, IC engines). In this section, we discuss the concepts of drop size distributions, moments of those distributions, and characteristic drop diameters computed from them. This is followed by a summary of methods available for describing drop size distributions.

Spray nozzles are used in many applications such as cleaning, cutting, and spraying. Spray nozzles come in many varieties, and are usually classified according to the specific mode of atomization they employ. In this chapter, twin fluid, swirl, hydraulic, ultrasonic, rotary, and electrostatic nozzles are discussed. First, their specific mode of atomization is explained, followed by a brief description on the variation on each type of nozzle. Next, a comprehensive list of performance correlations for each type of nozzle is compiled from various sources. Finally, these correlations are explored in more detail for each type of nozzle.

This chapter provides information on different types of drop-on-demand drop generators. It starts with thermal or bubble jets, in which a nucleation bubble is used to eject a droplet out of an orifice. This is followed by piezoelectric, pneumatic, microfluidic, electrohydrodynamics (EHD) and aerodynamic droplet generators. For each droplet generator, the principle of operation and major features and characteristics are described.

The working principle and the functioning of droplet stream generators are discussed. The essential feature of these generators is that the size of the droplets produced can be accurately controlled. This makes the generators important tools for setting initial or boundary conditions of the droplets in transport processes. Droplet sizes may range between 10 µm and the order of millimeters. Droplet streams and sprays produced with this technique may be very accurately monodispersed. Devices suitable for producing such droplet streams and sprays are presented and discussed. Ranges of the relevant operation parameters and spray properties are specified. Electric charging of the droplets allows the droplet trajectories to be controlled. Fields of application of the droplet stream generators, ranging from packaging to rapid prototyping and space applications, are addressed.

Plain orifice, or “pressure atomizers” are the most commonly used atomizers due primarily to their simplicity and ease of manufacture. This chapter provides background on the characteristics of these devices in terms of spray production and general behavior. Classical linear theories are reviewed to provide a basis for theoretical droplet size predictions. More recent developments assessing the unsteadiness within these devices, and its role in spray production, is also provided in subsequent discussion. The chapter closes with modern nonlinear simulations of spray production using modern numerical techniques.

Pintle injectors have been developed for applications in rocket propulsion, but could potentially have high flowrate in other applications due to their relative simplicity. The spray from a pintle injector is formed from the collision of radial jets of fluid issuing from the center of the pintle post with an annular sleeve of fluid travelling axially along the post. The resultant interactions produce a conical spray similar to a hollow cone swirl atomizer. This chapter reviews historical applications of pintle injectors and theoretical bases for their design.

This chapter provides a review on the penetration and atomization of liquid jets in subsonic crossflows (LJICF). More emphasis is put on the basic physics of the problem while a general overview of different types of research on the subject is presented. The categorization is based on the physics of the problem rather than the type of the studies (numerical, theoretical, or experimental) to help better understanding of the involving physics.

This chapter is an introduction to impinging jet atomizers, in which two or more jets are made to impinge on each other. High energy impingement of these jets results in the atomization of the liquid. The chapter provides the theory for the prediction of the sheet formed by the impingement of two jets, followed by estimates of droplet sizes based on the sheet thickness. This chapter also provides information on the mixing processes in impinging jet nozzles.

Prediction of droplet size and velocity distribution produced by splash plate requires information on the liquid sheet characteristics and its breakup process. This chapter focuses on the sheet produced by splash plate nozzles and their characteristics such as sheet breakup length and produced droplet size. It explains different flow regimes occurring in splash plate nozzles as well as various breakup lengths provided by different researchers. Sheet formation phenomenon is explained theoretically and at the end correlations for droplet size prediction are provided.

This chapter provides an introduction to electrosprays (ES). Electrosprays, also known as Electrohydrodynamic (EHD) sprays, are sprays created from the atomization of a bulk liquid due to electrostatic charging. The fundamental physics involved in such sprays is first introduced followed by results of experimental and theoretical characterization. Practical applications are briefly discussed with special attention paid to the use of electrospray in mass spectrometry where it is used as an ion source.

This chapter discusses several other types of atomizers that were not considered in the previous chapters. This includes “swirl nozzles, T-jet nozzles, and vibrating mesh nebulizers.” The droplet size correlations for different types of nozzles is provided in Chap. 24.

Modern internal combustion engines running on liquid fuels employ injection of the liquid as the means of delivering fuel to the engine. In spark-ignition (SI) engines, there may be port fuel injection (PFI), throttle-body injection (TBI), or direct injection (DI). In compression ignition (CI) engines, injection may be into the port as in homogeneous-charge compression ignition (HCCI) engines or into the chamber as in conventional diesel engines. Injection pressures vary from 2 to 3 bar in PFI engines to 2,000 bar or higher in conventional DI diesel engines. Injection systems may be electronically controlled as in PFI and common-rail injectors (CRIs), or mechanically controlled. Injectors, sprays, and modes of fuel–air mixing in the engines are reviewed in this chapter. Engines selected for detailed discussion are PFI homogeneous-charge SI engines, gasoline direct injection (GDI) SI engines, diesel engines, and low-temperature combustion compression-ignition engines.

Large-eddy simulation (LES) is a promising technique for accurate prediction of reacting multiphase flows in practical gas-turbine engines. These combustors involve complex physical phenomena of primary atomization of liquid sheet/jet and secondary breakup, droplet evaporation, turbulent mixing of fuel vapor with oxidizer, and combustion dynamics. This chapter summarizes advances made in modeling spray fields with LES of turbulent reacting flows in realistic combustor configurations. Specifically, details of subgrid models for droplet dynamics including breakup, evaporation, deformation, droplet dispersion, and finite-size droplets are presented in the context of an Eulerian–Lagrangian simulation methodology on unstructured grids. Effectiveness of LES with advanced spray models in predicting spray behavior in a patternation study of realistic Pratt and Whitney injector is described.

The science and technology underlying the process of melt atomization is introduced, paying particular attention to relevant thermal, solidification and other transport phenomena. Melt atomization has now been developed as one of major produce methods for various metal and alloy powder, and hence it is of both scientific and technological interest. The mechanisms of melt disintegration, the design of typical atomization devices, the influence of key process parameters, the thermal transport in the atomized droplets, and the characteristics of the size distribution are briefly described and discussed.

In conventional spray pyrolysis (CSP or simply SP), a solution is sprayed into a carrier gas forming small droplets; owing to the high temperature of the surrounding gas, the solvent is vaporized and the solute is precipitated on and within the droplets. If the air temperature is high enough, solute is decomposed to form final solid particles. A schematic diagram of the spray pyrolysis process is shown in Fig. 37.1 [1]. Spray drying (SD) is similar to spray pyrolysis, except that there is no chemical decomposition in SD and usually the process temperature is lower. SP and SD techniques may produce fully-filled or hollow particles depending on the operating conditions. In general, for most materials, hollow particles are formed if at the onset of solute precipitation on the droplet surface, the solute concentration at the droplet center is lower than the equilibrium saturation (Jayanthi et al. [2]). However, Chau et al. [3] showed that Jayanthi’s model is not applicable to the formation of NaCl particles.

Low-pressure spray pyrolysis (LPSP) has been developed by generating micrometer-sized droplets under low-pressure environment. Unlike the conventional spray pyrolysis (CSP), a variety of nanoparticles, ranging from metals, metal oxides, to composite materials can be directly formed in the LPSP process, which was considered to follow a one-droplet-to-multiple-particles (ODMP) principle. The low-pressure is the direct driving force for the formation of nanoparticles. Inside the LPSP process, the micrometer-sized droplets are assumed to undergo rapid solvent evaporation upon entering the low-pressure environment that induces a fast nucleation rate to form primary nanocrystals. The aggregation of these nanocrystals is limited due to very short residence time under low-pressure conditions. In addition, the gas evolution due to thermal reactions and pressures inside the droplets/dried particles caused by high drying rates, are considered to be the main reasons for the fragmentation of primary nanocrystals into final nanoparticles.

Flame spray pyrolysis (FSP) has been applied for the production of powders industrially. FSP allows production of powders with controlled characteristics at a high rate. In addition to the process parameters, several other factors are crucial for nanoparticle production. Precursor type, as an example, is an important factor determining the particle size. Using metalorganic precursors, particles in nano-sized order could be produced. While for aqueous salt precursors, atomizer type is critical. Two-fluid nozzle atomizers could be used to produce nanoparticles. Only submicron particles could be achieved by using ultrasonic nebulizers. The particle formation mechanism follows one-droplet-to-one-particle (ODOP) principle. If an organic additive, such as urea was added to the precursor, nanoparticles could be obtained. The thermal decomposition of organic additives facilitated the disintegration of primary particles producing nanoparticles. This mechanism refers to one-droplet-to-multiple-particles (ODMP) route.

In many industrial applications powdered materials are used for the manufacturing and development of commodities, products, parts, tools, instruments, etc. Examples are in powder metallurgy, in the development of gas sensors, solar cells, thermal barrier coatings, catalysts, pigments, and pharmaceuticals. While in some applications, particle size and size distribution, and particle crystallinity and grain size may be immaterial or irrelevant, in some other applications particle characteristics may play an important role in the characteristics and quality of the final products. It is generally agreed upon that no matter the particles are crystalline or amorphous, as the particle size decreases, the particle reactivity increases. Nanocrystalline materials (grain size < 100 nm), either in bulk or powder form, compared to the polycrystalline materials have enhanced properties, such as hardness, yield strength, corrosion resistance, etc. Therefore, nanocrystalline nanoparticles (grain and particle size < 100 nm), such as quantum dots have superior properties.

Respiratory illnesses are commonly treated with drugs delivered to the lungs as an inhaled aerosol. The inhaled aerosol route sometimes offers advantages over other routes such as injection or oral delivery. These advantages include rapid and predictable onset of action of drug, decreased adverse reactions, as well as safe and convenient delivery. However, the design of a device and formulation for reliable delivery of a pharmaceutical compound as an inhaled aerosol is more difficult than most other delivery routes. This is because of the need to transform the active ingredient into an aerosol having particle sizes of a few micrometers in diameter that is then supplied to the patient’s mouth upon inhalation. Devices that can create sprays with particles in the micrometer size range, but which remain portable, inexpensive to manufacture, easy to use by patients, and are robust enough to withstand patient use, are relatively few in design. Indeed, at present only four basic spray production mechanisms are currently in use on the clinical market for drug delivery to the lungs: pressurized release of a volatile propellant, colliding liquid jets, air-blast atomization and high frequency vibration methods. While other methods have undergone development (e.g., Rayleigh breakup of an extruded liquid jet [1]; high voltage electrosprays [2]), they have not yet reached market release. In the following we consider the four clinically available methods.

Water sprinkler sprays (with relatively large droplet sizes) in residential and commercial structures are probably the most well-known application of sprays in fire suppression. In more recent years, water mists (characterized by reduced droplet sizes, which may contain additives) have been considered as a replacement for Halon 1301, the most common fire suppressant chemical aboard aircraft and ships, but banned as an ozone-depleting chemical by the Montreal Protocol in 1987. Much research has focused on characterizing the liquid discharge from agent storage bottles, spray transport in various obstructed environments, agent suppression of liquid-fueled, spray-type fires, and determination of the effectiveness of various liquid and powdered chemicals (with respect to gaseous agents) to extinguish a flame in well-controlled experimental facilities. Research during the past two decades to characterize liquid and powdered sprays may find sprays appealing alternatives to environmentally harmful gaseous agents in the near future, if properly engineered.